Geometry and mesh for motor

Decide whether to draw the whole motor or just an 8th slice

pizza_slice = True

Define radii and points that help define the magnets, coils, and airgaps.

origin = (0,0)
# inner radius rotor
r1 = 26.5*10**(-3)
# outer radius rotor
r2 = 78.63225*10**(-3)
# sliding mesh rotor
r4 = 78.8354999*10**(-3)
# sliding mesh stator
r6 = 79.03874999*10**(-3)
# inner radius stator
r7 = 79.242*10**(-3)
# outer radius stator
r8 = 116*10**(-3)

# Points for magnet1 and air around magnet1
m1 = (69.23112999*10**(-3),7.535512*10**(-3))
m2 = (74.828958945*10**(-3),10.830092744*10**(-3))
m3 = (66.13621099700001*10**(-3),25.599935335*10**(-3))
m4 = (60.53713*10**(-3),22.30748*10**(-3))
a5 = (69.75636*10**(-3),5.749913*10**(-3))
a6 = (75.06735*10**(-3),3.810523*10**(-3))
a7 = (65.6868747*10**(-3),26.3184618*10**(-3))
# a7 = (65.3506200*10**(-3),26.51379*10**(-3))
a8 = (59.942145092*10**(-3),24.083661604*10**(-3))

# Points for magnet2 and air around magnet2
m5 = (58.579985516*10**(-3), 27.032444757*10**(-3))
m6 = (64.867251151*10**(-3),28.663475405*10**(-3))
m7 = (60.570096319*10**(-3),45.254032279*10**(-3))
m8 = (54.282213127*10**(-3),43.625389857*10**(-3))
a1 = (53.39099766*10**(-3),45.259392713*10**(-3))
a2 = (55.775078884*10**(-3),50.386185578*10**(-3))
a3 = (59.41521771*10**(-3),25.355776837*10**(-3))
a4 = (65.12210917100001*10**(-3),27.707477175*10**(-3))

# Points for Stator Nut and air in the stator
s1 = (79.04329892000*10**(-3),3.9538335974*10**(-3))
s2 = (80.143057128*10**(-3),4.0037794254*10**(-3))
s3 = (80.387321219*10**(-3),2.965459706*10**(-3))
s4 = (98.78501315600001*10**(-3),3.9007973292*10**(-3))
s5 = (98.44904989600001*10**(-3),9.026606148400001*10**(-3))
s6 = (80.086666706*10**(-3),7.5525611543*10**(-3))
s7 = (79.980020247*10**(-3),6.4912415424*10**(-3))
s8 = (78.88229587*10**(-3),6.4102654448*10**(-3))

Next, use the points to define drawing functions for the magnets and coils

import numpy as np
import netgen.occ as occ
from numpy import sin, cos, pi

def rotate(m,k,p):
    a = np.pi/p
    mx = m[0]*np.cos(k*a) -m[1]*np.sin(k*a)
    my = m[0]*np.sin(k*a) +m[1]*np.cos(k*a)
    return (mx, my, 0)

def drawMagnet1(k):
    m1new = rotate(m1,k,4); m2new = rotate(m2,k,4)
    m3new = rotate(m3,k,4); m4new = rotate(m4,k,4)

    a5new = rotate(a5,k,4); a6new = rotate(a6,k,4)
    a7new = rotate(a7,k,4); a8new = rotate(a8,k,4)

    #Draw magnet
    seg1 = occ.Segment(m1new,m2new); seg2 = occ.Segment(m2new,m3new)
    seg3 = occ.Segment(m3new,m4new); seg4 = occ.Segment(m4new,m1new)
    magnet1 = occ.Face(occ.Wire([seg1,seg2,seg3,seg4]))

    #Draw air around magnet
    air_seg1 = occ.Segment(m1new,a5new); air_seg2 = occ.Segment(a5new,a6new)
    air_seg3 = occ.Segment(a6new,m2new); air_seg4 = occ.Segment(m2new,m1new)
    air_magnet1_1 = occ.Face(occ.Wire([air_seg1,air_seg2,air_seg3,air_seg4]))

    air_seg5 = occ.Segment(m4new,m3new); air_seg6 = occ.Segment(m3new,a7new)
    air_seg7 = occ.Segment(a7new,a8new); air_seg8 = occ.Segment(a8new,m4new)
    air_magnet1_2 = occ.Face(occ.Wire([air_seg5,air_seg6,air_seg7,air_seg8]))

    return (magnet1,air_magnet1_1,air_magnet1_2)

def drawMagnet2(k):
    m5new = rotate(m5,k,4); m6new = rotate(m6,k,4)
    m7new = rotate(m7,k,4); m8new = rotate(m8,k,4)

    a1new = rotate(a1,k,4); a2new = rotate(a2,k,4)
    a3new = rotate(a3,k,4); a4new = rotate(a4,k,4)

    #Draw magnet
    seg1 = occ.Segment(m5new,m6new); seg2 = occ.Segment(m6new,m7new)
    seg3 = occ.Segment(m7new,m8new); seg4 = occ.Segment(m8new,m5new)
    magnet2 = occ.Face(occ.Wire([seg1,seg2,seg3,seg4]))

    #Draw air around magnet
    air_seg1 = occ.Segment(m5new,a3new); air_seg2 = occ.Segment(a3new,a4new)
    air_seg3 = occ.Segment(a4new,m6new); air_seg4 = occ.Segment(m6new,m5new)
    air_magnet2_1 = occ.Face(occ.Wire([air_seg1,air_seg2,air_seg3,air_seg4]))

    air_seg5 = occ.Segment(m8new,m7new); air_seg6 = occ.Segment(m7new,a2new)
    air_seg7 = occ.Segment(a2new,a1new); air_seg8 = occ.Segment(a1new,m8new)
    air_magnet2_2 = occ.Face(occ.Wire([air_seg5,air_seg6,air_seg7,air_seg8]))

    return (magnet2,air_magnet2_1,air_magnet2_2)

def drawStatorNut(k):

    s1new = rotate(s1,k,24); s2new = rotate(s2,k,24)
    s3new = rotate(s3,k,24); s4new = rotate(s4,k,24)
    s5new = rotate(s5,k,24); s6new = rotate(s6,k,24)
    s7new = rotate(s7,k,24); s8new = rotate(s8,k,24)

    #Draw stator coil
    seg1 = occ.Segment(s2new,s3new); seg2 = occ.Segment(s3new,s4new)
    seg3 = occ.Segment(s4new,s5new); seg4 = occ.Segment(s5new,s6new)
    seg5 = occ.Segment(s6new,s7new); seg6 = occ.Segment(s7new,s2new)
    stator_coil = occ.Face(occ.Wire([seg1,seg2,seg3,seg4,seg5,seg6]))

    #Draw air nut in the stator
    air_seg1 = occ.Segment(s1new,s2new); air_seg2 = occ.Segment(s2new,s7new)
    air_seg3 = occ.Segment(s7new,s8new); air_seg4 = occ.Segment(s8new,s1new)
    stator_air = occ.Face(occ.Wire([air_seg1,air_seg2,air_seg3,air_seg4]))

    stator_air = stator_air-(stator_air*air_gap_stator)
    return (stator_coil,stator_air)

Use the functions to define the shapes using the OCC technology.

domains = []

h_max = 1

h_air_gap = r6-r4 #0.05*h_max
h_air_magnets = h_max
h_coils = h_max
h_stator_air = h_max
h_magnets = h_max
h_stator_iron = h_max
h_rotor_iron = h_max
h_shaft_iron = h_max

rotor_inner  = occ.Circle(origin,r=r1).Face()
rotor_outer  = occ.Circle(origin,r=r2).Face()
sliding_inner  = occ.Circle(origin,r=r4).Face()
sliding_outer  = occ.Circle(origin,r=r6).Face()
stator_inner = occ.Circle(origin,r=r7).Face()
stator_outer = occ.Circle(origin,r=r8).Face()

rotor_inner.edges[0].name = "rotor_inner"
rotor_outer.edges[0].name = "rotor_outer"
stator_inner.edges[0].name = "stator_inner"
stator_outer.edges[0].name = "stator_outer"

rotor_iron = rotor_outer - rotor_inner

air_gap_stator = stator_inner - sliding_outer
air_gap = sliding_outer - sliding_inner
air_gap_rotor = sliding_inner - rotor_outer

stator_iron = stator_outer - stator_inner

for k in range(48):
    (stator_coil,stator_air) = drawStatorNut(k)

    stator_coil.faces.name = "coil" + str(k)
    stator_air.faces.name = "air"

    stator_iron -= stator_coil
    stator_iron -= stator_air

    domains.append(stator_coil)
    domains.append(stator_air)

for k in range(8):
    (magnet1,air_magnet1_1,air_magnet1_2) = drawMagnet1(k)
    (magnet2,air_magnet2_1,air_magnet2_2) = drawMagnet2(k)

    magnet1.faces.name = "magnet" + str(2*k+1)
    magnet1.faces.maxh = h_magnets
    magnet1.edges[0].name = "magnets_interface"
    magnet1.edges[1].name = "magnets_interface"
    magnet1.edges[2].name = "magnets_interface"
    magnet1.edges[3].name = "magnets_interface"

    magnet2.faces.name = "magnet" + str(2*k+2)
    magnet2.faces.maxh = h_magnets
    magnet2.edges[0].name = "magnets_interface"
    magnet2.edges[1].name = "magnets_interface"
    magnet2.edges[2].name = "magnets_interface"
    magnet2.edges[3].name = "magnets_interface"

    air_magnet1_1.faces.name = "rotor_air"
    air_magnet1_2.faces.name = "rotor_air"
    air_magnet2_1.faces.name = "rotor_air"
    air_magnet2_2.faces.name = "rotor_air"

    air_magnet1_1.faces.maxh = h_air_magnets
    air_magnet1_2.faces.maxh = h_air_magnets
    air_magnet2_1.faces.maxh = h_air_magnets
    air_magnet2_2.faces.maxh = h_air_magnets

    rotor_iron -= magnet1
    rotor_iron -= air_magnet1_1
    rotor_iron -= air_magnet1_2
    rotor_iron -= magnet2
    rotor_iron -= air_magnet2_1
    rotor_iron -= air_magnet2_2

    domains.append(magnet1)
    domains.append(magnet2)
    domains.append(air_magnet1_1)
    domains.append(air_magnet1_2)
    domains.append(air_magnet2_1)
    domains.append(air_magnet2_2)

stator_iron.faces.name = "stator_iron"
stator_iron.faces.maxh = h_stator_iron

air_gap_stator.faces.name = "air_gap_stator"
air_gap_stator.faces.maxh = h_air_gap

air_gap.faces.name = "air_gap"
air_gap.faces.maxh = h_air_gap

air_gap_rotor.faces.name = "air_gap_rotor"
air_gap_rotor.faces.maxh = 1.08*h_air_gap

rotor_iron.faces.name = "rotor_iron"
rotor_iron.faces.maxh = h_rotor_iron

shaft_iron = rotor_inner
shaft_iron.faces.name = "shaft_iron"
shaft_iron.faces.maxh = h_shaft_iron

domains.append(shaft_iron)
domains.append(rotor_iron)
domains.append(air_gap_stator)
domains.append(air_gap)
domains.append(air_gap_rotor)
domains.append(stator_iron)

geo = occ.Glue(domains)

if pizza_slice:
    pizza = occ.MoveTo(*origin).Line(1).Rotate(90).Line(1).Close().Face()

    geo = pizza*occ.Glue(domains)

    geo.edges[0].name = "left"
    geo.edges[4].name = "left"
    geo.edges[24].name = "left"
    geo.edges[28].name = "left"
    geo.edges[32].name = "left"
    geo.edges[96].name = "left"

    geo.edges[2].name = "right"
    geo.edges[6].name = "right"
    geo.edges[26].name = "right"
    geo.edges[30].name = "right"
    geo.edges[46].name = "right"
    geo.edges[98].name = "right"

    rot = occ.Rotation(occ.Axis((0,0,0), occ.Z), 45)
    geo.edges[2].Identify(geo.edges[0], "per", 0, rot)
    geo.edges[6].Identify(geo.edges[4], "per", 0, rot)
    geo.edges[26].Identify(geo.edges[24], "per", 0, rot)
    geo.edges[30].Identify(geo.edges[28], "per", 0, rot)
    geo.edges[46].Identify(geo.edges[32], "per", 0, rot)
    geo.edges[98].Identify(geo.edges[96], "dsa", 0, rot)

geoOCC = occ.OCCGeometry(geo, dim=2)
geoOCCmesh = geoOCC.GenerateMesh()

import ngsolve as ng
ngsolvemesh = ng.Mesh(geoOCCmesh)
ngsolvemesh.Refine()
# ngsolvemesh.Refine()
# geoOCCmesh.SecondOrder()

from netgen.webgui import Draw as DrawGeo
DrawGeo(geo)

BaseWebGuiScene

#ngsolvemesh.Refine()

mesh = ngsolvemesh
plist = []
for pair in mesh.ngmesh.GetIdentifications():
    plist += list(mesh.vertices[pair[0]-1].point) + [0]
    plist += list(mesh.vertices[pair[1]-1].point) + [0]

from ngsolve.webgui import Draw as DrawMesh
DrawMesh(mesh, objects=[{"type" : "lines", "position" : plist, "name": "identification", "color": "purple"}])

BaseWebGuiScene

#####################################################################################################################
Mperp_mag1 = np.array([-0.507223091788922, 0.861814791678634])
Mperp_mag2 = np.array([-0.250741225095427, 0.968054150364350])
Mperp_mag3 = (-1)*np.array([-0.968055971101187, 0.250734195544481])
Mperp_mag4 = (-1)*np.array([-0.861818474866413, 0.507216833690415])
Mperp_mag5 = np.array([-0.861814791678634, -0.507223091788922])
Mperp_mag6 = np.array([-0.968054150364350, -0.250741225095427])
Mperp_mag7 = (-1)*np.array([-0.250734195544481, -0.968055971101187])
Mperp_mag8 = (-1)*np.array([-0.507216833690415, -0.861818474866413])
Mperp_mag9 = np.array([0.507223091788922, -0.861814791678634])
Mperp_mag10 = np.array([0.250741225095427, -0.968054150364350])
Mperp_mag11 = (-1)*np.array([0.968055971101187, -0.250734195544481])
Mperp_mag12 = (-1)*np.array([0.861818474866413, -0.507216833690415])
Mperp_mag13 = np.array([0.861814791678634, 0.507223091788922])
Mperp_mag14 = np.array([0.968054150364350, 0.250741225095427])
Mperp_mag15 = (-1)*np.array([0.250734195544481, 0.968055971101187])
Mperp_mag16 = (-1)*np.array([0.507216833690415, 0.861818474866413])

Mperp_mag = np.c_[Mperp_mag1,Mperp_mag2, Mperp_mag3, Mperp_mag4, Mperp_mag5, Mperp_mag6, Mperp_mag7, Mperp_mag8,
                  Mperp_mag9,Mperp_mag10,Mperp_mag11,Mperp_mag12,Mperp_mag13,Mperp_mag14,Mperp_mag15,Mperp_mag16]

m = np.c_[Mperp_mag[1,:],-Mperp_mag[0,:]].T
nu0 = 10**7/(4*np.pi)
m = m*nu0*1.158095238095238
#####################################################################################################################




#####################################################################################################################
offset = 0
polepairs  = 4
gamma_correction_model = -30.0
gamma = 40.0
gamma_correction_timestep = -1
phi0 = (gamma + gamma_correction_model + gamma_correction_timestep * polepairs) * np.pi/180.0



def f48(s):
    return (s-1)%48

area_coils_UPlus  = np.r_[f48(offset+1) , f48(offset+2)]
area_coils_VMinus = np.r_[f48(offset+3) , f48(offset+4)]
area_coils_WPlus  = np.r_[f48(offset+5) , f48(offset+6)]
area_coils_UMinus = np.r_[f48(offset+7) , f48(offset+8)]
area_coils_VPlus  = np.r_[f48(offset+9) , f48(offset+10)]
area_coils_WMinus = np.r_[f48(offset+11), f48(offset+12)]

for k in range(1,4):
    area_coils_UPlus = np.r_[area_coils_UPlus, f48(k*12+offset+1)]
    area_coils_UPlus = np.r_[area_coils_UPlus, f48(k*12+offset+2)]

    area_coils_VMinus = np.r_[area_coils_VMinus, f48(k*12+offset+3)]
    area_coils_VMinus = np.r_[area_coils_VMinus, f48(k*12+offset+4)]

    area_coils_WPlus = np.r_[area_coils_WPlus, f48(k*12+offset+5)]
    area_coils_WPlus = np.r_[area_coils_WPlus, f48(k*12+offset+6)]

    area_coils_UMinus = np.r_[area_coils_UMinus, f48(k*12+offset+7)]
    area_coils_UMinus = np.r_[area_coils_UMinus, f48(k*12+offset+8)]

    area_coils_VPlus = np.r_[area_coils_VPlus, f48(k*12+offset+9)]
    area_coils_VPlus = np.r_[area_coils_VPlus, f48(k*12+offset+10)]

    area_coils_WMinus = np.r_[area_coils_WMinus, f48(k*12+offset+11)]
    area_coils_WMinus = np.r_[area_coils_WMinus, f48(k*12+offset+12)]


I0peak = 1555.63491861 ### *1.5
phase_shift_I1 = 0.0
phase_shift_I2 = 2/3*np.pi#4/3*pi
phase_shift_I3 = 4/3*np.pi#2/3*pi

I1c = I0peak * np.sin(phi0 + phase_shift_I1)
I2c = (-1)* I0peak * np.sin(phi0 + phase_shift_I2)
I3c = I0peak * np.sin(phi0 + phase_shift_I3)

areaOfOneCoil = 0.00018053718538758062

UPlus  =  I1c* 2.75 / areaOfOneCoil
VMinus =  I2c* 2.75 / areaOfOneCoil

WPlus  =  I3c* 2.75 / areaOfOneCoil
UMinus = -I1c* 2.75 / areaOfOneCoil

VPlus  = -I2c* 2.75 / areaOfOneCoil
WMinus = -I3c* 2.75 / areaOfOneCoil

j3 = np.zeros(48)
j3[area_coils_UPlus]  = UPlus
j3[area_coils_VMinus] = VMinus
j3[area_coils_WPlus]  = WPlus
j3[area_coils_UMinus] = UMinus
j3[area_coils_VPlus]  = VPlus
j3[area_coils_WMinus] = WMinus
#####################################################################################################################

import sys
sys.path.insert(0,'../../../') # adds parent directory

import pde
import plotly.io as pio
pio.renderers.default = "notebook"


MESH = pde.mesh.netgen(geoOCCmesh)

ind_air_all = np.flatnonzero(np.core.defchararray.find(MESH.regions_2d,'air')!=-1)
ind_stator_rotor = np.flatnonzero(np.core.defchararray.find(MESH.regions_2d,'iron')!=-1)
ind_magnet = np.flatnonzero(np.core.defchararray.find(MESH.regions_2d,'magnet')!=-1)
ind_coil = np.flatnonzero(np.core.defchararray.find(MESH.regions_2d,'coil')!=-1)
ind_shaft = np.flatnonzero(np.core.defchararray.find(MESH.regions_2d,'shaft')!=-1)

trig_air_all = np.where(np.isin(MESH.t[:,-1],ind_air_all))
trig_stator_rotor = np.where(np.isin(MESH.t[:,-1],ind_stator_rotor))
trig_magnet = np.where(np.isin(MESH.t[:,-1],ind_magnet))
trig_coil = np.where(np.isin(MESH.t[:,-1],ind_coil))
trig_shaft = np.where(np.isin(MESH.t[:,-1],ind_shaft))

vek = np.zeros(MESH.nt)
vek[trig_air_all] = 1
vek[trig_magnet] = 2
vek[trig_coil] = 3
vek[trig_stator_rotor] = 4
vek[trig_shaft] = 3.6

# fig = MESH.pdemesh()
# fig = MESH.pdesurf(vek)
# fig.show()